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Lecture 8 Stability and Latent Heat

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Lecture 8 Stability and Latent Heat MET 200 Lecture 8 Stability Quiz 1 Results 9 8 7 6 5 4 3 2 1 0 >90 >80 >70 >50 M Student Count vs Percent 1 2 Previous Lecture Cloud classification Clouds are categorized by their height, appearance, and vertical development – High Clouds - generally above 16,000 ft at middle latitudes (>6 km) • Main types - Cirrus, Cirrostratus, Cirrocumulus – Middle Clouds – 7,000-23,000 feet (2-6 km) • Main types – Altostratus, Altocumulus – Low Clouds - below 7,000 ft (<2 km) • Main types – Stratus, stratocumulus, nimbostratus – Vertically developed clouds (via convection) • Main types – Cumulus, Cumulonimbus Cloud forms and what they tell us. 3 4 Cloud type summary Vertically developed clouds Cumulus • Puffy “cotton” • Flat base, rounded top • More space between cloud elements than stratocumulus Cumulonimbus • Thunderstorm cloud • Very tall, often reaching tropopause • Individual or grouped • Large energy release from water vapor condensation 5 6 Lecture 8 Hot Air Rises Stability Defining Stability Buoyancy in the atmosphere (hot air rises) Environmental vs Parcel Lapse Rates 7 8 Hydrostatic Balance Hydrostatic Equation What keeps air from rising despite the strong upward pressure gradient force? The vertical component of the momentum equation can be rewritten after elimination of small terms. A balance between gravity ∂p and the pressure gradient = −ρg force. ∂z Pressure gradient Since g is a constant, this equation tells us that the rate of change of pressure with height is dependent on air density or temperature: it is greater for cold dense air than for warm less dense air. Gravity € This equation is used to diagnose altitude above the ground based on the pressure distribution. 9 10 Stability in the Atmosphere Stability in the Atmosphere Warm (cold) air relative to its surroundings will rise (sink). To determine the atmosphere’s stability for vertical motions we need to compare the temperature of rising/sinking air parcels with the temperature of the air in the surrounding environment. An Initial Stable Unstable Neutral Perturbation Returns Keeps Stays at Going new level How do we diagnose stability in the atmosphere? What assumptions are implicit to our analysis of soundings for stability? 11 12 Lapse Rates Derive the Dry Adiabatic Lapse Rate A lapse rate is a change of temperature with height in the Start with 1st law of thermodynamics, the total energy of an atmosphere. There are three kinds of lapse rates: isolated system is constant. The change in the internal 1.Environmental Lapse Rates are measured by a energy of a closed system is equal to the amount of heat thermistor on a weather balloon. supplied to the system from the outside, minus the amount 2.Dry adiabatic lapse rate is the change of of work derived from the system. temperature that a dry or clear air parcel experiences when it moves up or down. An adiabatic process assumes no heat exchange occurs across the parcel’s boundary. 3.Moist adiabatic lapse rate occurs in a cloud because latent heat is released, so the temperature cools more slowly in a rising air parcel. 13 14 Parcel Lapse Rates:Why Rising Air Cools Derive the Dry Adiabatic Lapse Rate Start with 1st law of thermodynamics, energy added = change in internal energy - work. Then make adiabatic assumption, and assume hydrostatic balance. 1st Law of Thermodynamics : dq = cpdT - αdp Adiabatic assumtion: cpdT = αdp Hydrostatic assumption: αdp = -gdz Combining these two equations to eliminate the pressure, one arrives at the result for the DALR: cpdT = -gdz Therefore Γd = dT/dz = -g/cp • Rising air parcels expand. • Work done by air molecules in the parcel pushing outward consumes energy and lowers the parcel temperature. 15 16 Parcel Lapse Rates:Why Rising Air Cools Saturated Adiabatic Non-convectively Lift to the LCL Lapse Rate Varies with Height Moist Adiabat Td T – Average SALR in lower troposphere is ~ 6˚ C/km – SALR depends on saturation vapor pressure which depends on T and P. – Since saturation vapor pressure varies exponentially with increasing temperature, the saturated adiabatic LR is not constant, rather it varies from ~ 3-9˚ C/km. A saturated rising air parcel cools less than an unsaturated – Thus, the SALR is curved, approaching the DALR in the upper parcel because latent heat is released when drops form. troposphere as the temperature of the parcel drops. 17 18 Saturated Adiabatic Lapse Rate Determining Convective Cloud Bases • Dry air parcels cool at the dry adiabatic rate (about 10˚C/km) • Dew point decreases at a rate of ~ 2˚C/km • This means that the dew point approaches the air parcel temperature at a rate of about 8˚C/km • If the dew point depression were 4˚C at the surface, a cloud where: base would appear at a height of 500 meters Γw = Saturated adiabatic lapse rate, K/m –Cloud base occurs when dew point = temp (100% RH) 2 g = Earth's gravitational acceleration = 9.8076 m/s • Each one degree difference between the surface Lv = Heat of vaporization of water, J/kg temperature and the dew point will produce an increase in r = Mixing Ratio: The ratio of the mass of water vapor to the mass of dry air, kg/kg −1 −1 the elevation of cloud base of 125 meters Rd = Specific gas constant of dry air = 287 J kg K ε =The dimensionless ratio of the specific gas constant of dry air to the specific gas constant for water vapor = 0.6220 T = Temperature of the saturated air, K −1 −1 cp = The specific heat of dry air at constant pressure, J kg K 19 20 Orographic Clouds The Key to Determining Stability • To test for stability we need to compare the changing temperature of air parcels with their environments. • Parcel Lapse Rates are fixed by physics. • Environmental lapse rates are not fixed, they are always changing, depending on wind, sun, etc. • Therefore, the key to determining atmospheric stability is the slope, or magnitude, of the environmental lapse rate. • Forced lifting along a topographic barrier causes air parcel expansion and cooling • Clouds & precipitation often develop on upwind side of Mts. • Air dries and warms during descent on downwind side 21 22 Comparison of Environmental and Conditions that contribute to Parcel Lapse Rates a stable atmosphere 1. Absolutely stable - if they Radiative cooling of have a value less than surface at night the moist lapse rate. Advection of cold air 2. Conditionally unstable - if near the surface. they fall between the dry and moist adiabatic lapse Air moving over a rates. cold surface (e.g., snow) 3. Absolutely unstable - if they have a value greater Adiabatic warming than the dry adiabatic due to compression lapse rate. from subsidence (sinking). 23 24 Conditions that contribute to Cloud Loop for 9/24/09 a stable atmosphere When a layer of air sinks an inversion forms below. This is the cause of the tradewind inversion common over Hawaii. Lihue Temperature Chart from 9/24/09 (AKA Skew-T Chart) 25 26 Radiation Inversion Temperature Inversions • Radiation inversions feature • A temperature inversion is simply a layer in the increasing T with height above atmosphere in which the temperature increases with ground height. • Occur on most clear, calm • All temperature inversions are absolutely stable. • nights (nocturnal inversion) • Temperature inversions prevent vertical mixing of air Are strongest when and can contribute to pollution episodes. • Winds are calm • Air is dry and cloud free • Less IR absorption • Less latent heat release from fog/ dew formation • Night is long 27 28 Absolutely Stable Absolutely Stable Air • When the environmental lapse rate is less than the moist and dry adiabatic lapse rates, the atmosphere is absolutely stable. • Temperature inversions (increasing temperature with height) are absolutely stable, and result in reduced mixing. In clear air In cloudy air 29 30 Conditions that Enhance Atmospheric Instability? Conditionally Unstable Air • What if the • Cooling of air aloft environmental lapse – Cold advection aloft rate falls between the – Radiative cooling of air/clouds moist and dry adiabatic aloft lapse rates? • Warming of surface air – The atmosphere is – Solar heating of ground unstable for saturated air – Warm advection near surface parcels but stable for – Air moving over a warm surface unsaturated air parcels (e.g., a warm body of water) – This situation is termed • Contributes to lake effect snow conditionally unstable • Lifting of a layer of air • This is the typical – Especially if bottom of layer is situation in the moist and top is dry atmosphere 31 32 Cumulonimbus Conditionally Unstable Air Clear Air - Stable Cloudy Air - Unstable 33 34 Absolutely Unstable Absolutely Unstable Air • The atmosphere is absolutely unstable if the environmental lapse rate exceeds the moist and dry adiabatic lapse rates. • This situation is not long- lived. – Usually results from surface heating and is confined to a shallow layer near the surface. – Vertical mixing can eliminate it. In clear air In cloudy air 35 36 Absolute Instability (example) Mirage and Absolute Instability Jogger on calm, summer day may have 122 F at their feet and 90 F at their waist! 37 38 Cumulus Schematic for a Trade Wind Cumulus Cloud 39 40 Stability of Dry (Clear) Air A saturated rising air parcel cools less than an unsaturated parcel Atmospheric stability depends on the • If a rising air parcel becomes saturated environmental lapse rate condensation occurs and a cloud forms. –A rising unsaturated air parcel • Condensation warms the air parcel due to the cools according to the dry adiabatic lapse rate release of latent heat. –If this air parcel is • So, a rising parcel cools less if it is saturated (e.g., • warmer than surrounding air, it in cloud). is less dense and buoyancy accelerates the parcel upward. • Define a moist adiabatic lapse rate • colder than surrounding air, it – ~ 5˚ C/1000 m is more dense and buoyancy – Not constant (varies from ~ 3-9˚ C) forces oppose the rising motion.
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